dc electrical resistivity · 2020-05-21 · dc electrical resistivity method: • apply a direct...
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DC Electrical ResistivityMethod: • Apply a direct current (or very low frequency alternating current) to the Earth using a dipole current source/sink• Measure voltage across a pair of electrode probes
The measured voltage represents a difference in potential… Advantage: Instrumentation doesn’t require great sensitivity!
Source Sinki
Current (charge) flow
Electricalequipotential
+ –V
Similar to gravity and magnetics, DC resistivity is a potential field method:
DC Electrical Resistivity
Source Sinki
Current (charge) flow
Electricalequipotential
Ohm’s Law:
So for a given current i and electrode spacing d (defines ), V depends on
d
+ –V
DC Electrical Resistivity
1 10 1000 104 105 106100
Resistivity ( m)
clay
topsoil
shale
porous limestone
dense limestone
metamorphic rocks
igneous rocks
graphitic schist
gravel
weathered bedrock
gabbro
sandstone
Resistivity properties of rocks & soils:
Sulfides
Temperature
Water Salinity in Pore Fluids
Example: Current source I in an infinite homogeneous medium with constant resistivity
We expect V = 0 at r = , & equipotential surfaces to be spherical around the source (similar to gravity!)
So, by Ohm's Law:
for some unknown, A. We can express A in terms of the ground current,
so that,
Now, integrating V/r = A/r2 = I/(4r2), we finally obtain:
or, equivalently:
So given a known I & a measured voltage at known r, we can solve for a constant resistivity .
A I4
I4
V I4r
4rVI
More realistic representation of Earth is a halfspace:
Same current is forced into half the volume so
or equivalently
And for two current electrodes +I and –I, total potential is given by the sum of the two point sources
r1 r2
V
+
+ –
Vz z 0
0
V I2r
2rVI
In practice we measure voltage difference at two points, V = Va – Vb
1
2
ab
We are really interested however in imaging a subsurface in which varies. The potentials integrate over the volume so they provide information relevant for doing exactly that!
Electrode Arrays: Arrangement of the electrodes
Wenner Array: (Classical: common in older surveys)
IV a
Constant spacing (“a-spacing”):
r1a = r2b = a r1b = r2a = 2a
aa
Wenner-Lee Array:I
a
Additional voltage measurements to a center electrode reduce sensitivity to near-surface resistivity variations
a
aV1
V2 V3
I V
2s
a
Schlumberger Array:
Also less sensitive to near-surface resistivity variations, & required half the effort to move electrodes for sounding studies (of vertical changes in resistivity)
Dipole-Dipole Array:I
Requires larger current source, but fairly common now with the development of multichannel instruments
V
Pole-Dipole Array:
Most sensitive to resistivity in the shell between radii r1 & r2 – commonly used for tunnel/karst detection
V
I r1
r2
Telford et al. 1990
Modeling
Current penetration for a layer over half-space:
Current penetration into the second layer depends on depth of layer interface, & resistivities. Fraction of total current that penetrates below depth of an interface, z, is (for a Wenner array):
2
1
where a is electrode spacing, and
k 2 1
2 1
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
-1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00
Resistivity Ratio k
Fra
cti
on
of
Cu
rren
t2
1
z = a
z = 3a/2
z = 3a
k 2 1
2 1
Layer over half-space: Apparent resistivity for a Wenner array:
app ~ for a/z small
~ 2 for a/z large
Wenner Array: “Universal Curves"
Layer over a half-space: app depends only on the ratios (2 /1), and (a /d1)
Two-layer over half-space: Apparent resistivity for the for various half-space resistivity values.
Two-layer over half-space: Dependence of apparent resistivity on the thickness of the middle layer.
May or may not pick up sandwiched layer depending on thickness, contrast
For 3+ layers:
Rule of thumb: If layer thickness < 0.1 the depth to top of layer, it cannot be resolved. Also, solution from sounding can be highly non-unique
But resolution also depends on resistivity contrast: thicker layers may not be resolved if contrast is too small; transition of apparent resistivity versus a-spacing is much sharper for a resistive layer over a conductive layer than for the opposite.